We present and investigate a novel approach towards broad-bandwidth near-field scanning optical spectroscopy based on an in-line interferometer for homodyne mixing of the near field and a reference field. In scattering-type scanning near-field optical spectroscopy, the near-field signal is usually obscured by a large amount of unwanted background scattering from the probe shaft and the sample. Here we increase the light reflected from the sample by a semi-transparent gold layer and use it as a broad-bandwidth, phase-stable reference field to amplify the near-field signal in the visible and near-infrared spectral range. We experimentally demonstrate that this efficiently suppresses the unwanted background signal in monochromatic near-field measurements. For rapid acquisition of complete broad-bandwidth spectra we employ a monochromator and a fast line camera. Using this fast acquisition of spectra and the in-line interferometer we demonstrate the measurement of pure near-field spectra. The experimental observations are quantitatively explained by analytical expressions for the measured optical signals, based on Fourier decomposition of background and near field. The theoretical model and in-line interferometer together form an important step towards broad-bandwidth near-field scanning optical spectroscopy.
© 2017 Optical Society of America
One of the aims of optical near-field spectroscopy is to study the optical properties of nanostructures by resonant light scattering, localized to a nanometric volume far below the diffraction limit [1–4]. Ideally, near-field spectroscopy should enable broadband spectroscopic investigation at the single emitter level and may, in combination with ultrafast pump-probe measurement schemes [5–7], shed light on the dynamics of primary light-induced processes such as light harvesting and photo-catalytic surface reactions.
Such sub-diffraction-limit spectroscopy can be accomplished by focusing light into a diffraction-limited spot on the sample and by scattering light from the near field around a quantum emitter into the far field, either using an aperture-based probe or an aperture-less, pointed probe [8–10]. While light-guiding probes require a trade-off between throughput and lateral resolution [1,11], a principally smaller resolution is achieved when a solid metal or dielectric probe is brought near the emitter. In this aperture-less or scattering-type SNOM (s-SNOM), light from the near field is scattered into the far field, where it can be collected by a detector. The lateral resolution of tip-enhanced near-field spectroscopy is determined by the size of the probe apex of down to 10 nm [12,13], and can be even smaller, if the processes under observation depend on the field strength in a nonlinear fashion or when light localization by means of gap modes is used [3,14–16].
Typically in s-SNOM, a diffraction-limited laser focus simultaneously illuminates both the sample and the probe, a sharp metal or dielectric tip. Light is scattered from the near field of emitters in the vicinity of the tip, but also directly from the tip shaft as well as the sample. This directly scattered light usually causes a large background signal, obscuring the orders of magnitude smaller near-field signal. In principle, the background signal can be largely avoided by employing adiabatic nanofocusing to SNOM [17,18]. This technique is an active topic of current research and first applications in broadband light scattering and time-resolved spectroscopy are currently pursued in different laboratories [19,20]. Regular s-SNOM is already much better understood. Specifically, some effort has been devoted in the past to distinguishing the near-field signal from the background in s-SNOM [21–26]. In a very common approach, the tip-sample distance is modulated with a frequency typically in the 10-kHz-range . Due to the highly nonlinear dependence of the scattered near-field signal on the tip-sample distance, higher harmonics of the modulation frequency are found in the signal. Demodulating at higher harmonics improves the near-field to background ratio and leads to improved contrast .
However, even with demodulation at higher harmonic frequencies, a complete suppression of the unwanted background is challenging. Generally, the light field components that are scattered from the near field, from the diffraction-limited spot on the sample and from the tip shaft interfere and lead to the detection of a mixed intensity signal that cannot be disentangled, because mixing occurs at the electric field level [22,25,28]. In order to enable such discrimination of the different contributions to the signal and to eliminate the background signal, amplification of the near-field signal by mixing of the scattered signal with a well-controlled reference wave was introduced. In principle, the simplest way to achieve such amplification is by homodyne mixing via a Michelson interferometer . This interference, however, requires a highly stable interferometer. In particular at visible wavelengths, active stabilization is generally unavoidable, while in the infrared wavelength region high mechanical stability may be sufficient. A more robust approach is heterodyne mixing with a reference wave that was frequency-shifted with an acousto-optic modulator (AOM) [25,28]. The same principle can be realized without the need for an AOM in a pseudo-heterodyne mixing scheme, where a reference light wave is supplied with a sinusoidal phase modulation via a vibrating mirror in a Michelson interferometer .
This poses two considerable experimental challenges to broadband s-SNOM spectroscopy in the visible spectral range. Firstly, the background signal has to be suppressed efficiently and over a broad spectral range by mixing with a broad-bandwidth reference field. Secondly, this reference field is required to remain phase-stable with respect to the optical field scattered from the tip apex over a sufficiently long time to scan a sample.
Here we propose and experimentally demonstrate an efficient and easy-to-implement solution to both challenges. We deposit the sample under investigation on a homogeneous, semitransparent gold layer covered with a thin dielectric sheet. When illuminating the tip-sample region with a broadband light source transmitted through the gold film, this creates an inherently phase-stable in-line interferometer. The reflection from the gold film provides a reference field with an amplitude that largely exceeds that of spurious background fields. Near-field spectra recorded at higher modulation orders of the periodic modulation of the tip-sample distance thus predominantly probe the spectrum of the local near-field scattered from the tip-sample interaction region. In contrast, spectra recorded at lower modulation orders are governed by background fields scattered from the tip shaft. These spectra reveal a highly complex spectral modulation resulting from multiple-field interferences. Our results open up a new approach towards quantitative, ultrahigh resolution, broadband near-field scattering spectroscopy.
2. Experimental setup and measurement principle
Our experimental setup is in principle a back-scattering type SNOM, depicted schematically in Fig. 1. In order to study the near-field optical properties of our in-line interferometer, we first performed quasi-monochromatic measurements using a narrow-bandwidth laser, and later equipped the setup with a broad-bandwidth laser source and a spectrally resolving detector.
First, for quasi-monochromatic measurements, light from a Titanium:Sapphire laser (Spectra Physics, Tsumani) supplying pulses with a relatively narrow spectral bandwidth of around 20 nm centered at a wavelength of 780 nm is used to illuminate the sample. The light is linearly polarized, and the direction of the electric field vector is controlled by a half-wave plate (HWP) in a motorized rotation holder. To adjust the position of the focus precisely, a steering mirror equipped with two piezo actuators is employed in a 4f imaging system, consisting of two lenses with the same focal length of 50 mm. The tilt of the beam induced by the steering mirror is imaged onto the back focal plane of the microscope objective (MO) with a numerical aperture (NA) of 0.95. This results in a displacement of the beam in the MO focal plane, without distorting the focus. The light passes a 50:50 beam splitter (BS) and is then focused onto the far side of the sample, i.e., through a 150-µm thick quartz microscope slide onto the exit side of the slide. In this study we compare three different samples, for which the far side of the sample is either an uncoated quartz surface, the quartz surface covered with a semitransparent (~20-nm thick) gold film, or a semitransparent gold film covered with a ~200-nm thick SiO2 film. Positioning the focus position along the z-axis, perpendicular to the sample surface, is achieved by piezo-controlling the MO position.
A sharply etched gold taper is brought in close proximity to the sample surface in order to interact with and scatter light out of the near-field region. The laser focus is adjusted on the taper apex by maximizing the back-scattered light. Note that when scanning or when varying the tip-sample distance, the focus position remains on the apex of the gold nanotaper, while the sample is moved towards or away from the tip. The light that is scattered from the focus region is collected in backwards direction by the same MO, and the part reflected by the BS is collected by a lens (L3) and detected using an avalanche photodiode (APD, Hamamatsu C5331-02).
The single-crystalline gold nanotips are produced from polycrystalline, 99.99%-gold wire with a diameter of 125 µm. The gold wire is annealed and electrochemically etched as described in . The process typically results in tapers with a very smooth surface, with an opening angle of around 30°, and in a sharp apex with a radius of curvature of about 10 nm. Such a sharp gold tip is glued onto a tuning fork, which is driven by an AC voltage at its resonance frequency kHz. The tuning fork amplitude is set such that the tip moves back and forth along the taper axis over a distance of about 30 nm. The tip is then brought in close proximity to the sample, such that the tip is aligned with its axis perpendicular to the sample surface. The tip-sample distance is controlled by adjusting the sample z-position using the tuning fork oscillation amplitude as the feedback signal in a tapping-mode atomic force microscope. The signal detected in back reflection by the APD is processed using a lock-in amplifier (Zurich Instruments HFLI) and using the tip modulation frequency as the reference signal. In this work, typically the signal demodulated at the fundamental tip modulation frequency , as well as the signals demodulated at its second, third, and fourth harmonic are recorded. To determine the DC field strength, the APD is substituted by a silicon photodiode (SiPD, Thorlabs PDA36A) and its signal is recorded without lock-in detection, which basically yields the unmodulated signal .
Finally, for broad-bandwidth spectroscopic measurements the narrow-bandwidth laser is substituted with a titanium:sapphire laser (Femtolasers Rainbow) with a spectral bandwidth exceeding 100 nm. Instead of measuring with the APD and lock-in detector the light is spectrally dispersed using a monochromator (Princeton Instruments, Acton SP2150i with 300-lines/mm grating) equipped with a fast line camera (e2V Aviiva EM4 with 512 pixels). This line camera enables acquisition of spectra with a rate of 210 kHz, such that by post-processing the data pixel-wise we can extract complete spectra demodulated up to the fourth harmonic.
In the following sections describing the measurements and the analysis of the signals to we assume the detected signal to consist of the following electric field components (see the right-hand side of Fig. 1): First, light is directly reflected off the far side surface of the microscope slide. This direct reflection is rather weak in the case of the uncoated quartz sample and up to ~50% of the incident light in the case that the quartz substrate is coated with a semitransparent gold film, and is used as our reference field . The light that is transmitted through the substrate is partly scattered from the tip shaft, causing a background light contribution . If the tip is in close proximity to the sample surface, it interacts with the sample’s near field region, scattering light to the far field. This interaction contributes the near-field component to the detected signal.
3. Quasi-monochromatic measurements
We record the signals to with the setup as described above as a function of the distance between tip and sample. The tip-sample distance is controlled by adjusting the sample z-position. The approach is stopped when the tuning fork oscillation amplitude is reduced by 5%, which we take as the point of contact or zero distance. We record such approach curves for three different samples, namely for a quartz surface covered with a semitransparent (~20-nm thick) gold film, for an uncoated quartz surface, and for a quartz surface covered with a ~200-nm thick SiO2 film on top of the ~20-nm thick semitransparent gold film.
Figures 2(a) and 2(b) show the optical signals when the sample with the semi-transparent gold film is approached to the tip. The unmodulated signal , which is measured using the SiPD and without lock-in detection, displays a weak modulation with a period of ~390 nm, corresponding to half the wavelength of the excitation laser [see the red fit curve of a sinusoidal function on top of a linear function, plotted together with the experimentally measured black curves in Fig. 2(a)]. This modulation is a result of the interference of the light reflected from the tip shaft, , and from the gold-coated surface of the substrate facing the tip, . This modulation is weak, because the electric field strength of is only a small fraction of that of . Furthermore, decreases steadily as the reflecting gold surface is moved out of the laser focus, causing the constant slope underneath the modulation. As expected, a near-field contribution cannot be discerned in the DC optical signal.
The experiment is repeated with the APD and lock-in detector, and the demodulated signals to are recorded as a function of tip-sample distance. Figure 2(b) shows the amplitude of the lock-in-detector signal during the approach at the respective demodulation frequency, for the gold-coated sample. The optical signal demodulated at the fundamental tip modulation frequency, [blue curve in Fig. 2(b)], still shows a strong modulation for both samples, now at a period of a quarter wavelength due to plotting the amplitude of the lock-in signal. The optical signal demodulated at the second harmonic, (not shown in Fig. 2 for the sake of clarity), shows a similar behavior and has an amplitude comparable to that of . When demodulating at the third harmonic, however, (green curve) still shows some modulation, but the amplitude is reduced by roughly a factor 4. Finally, demodulating at the fourth harmonic (red curve), the amplitude of is not above noise level.
In close vicinity to the gold surface [compare the steep decrease of the tuning fork amplitude, i. e., the black curve in the inset in Fig. 2(b)], a weak deviation from the sinusoidal curve by less than 15% is discernible on the first-harmonic optical signal , and there is a clear near-field contribution apparent of both and . The near-field signal resembles a strong exponential signal increase with a -decay length of 8 nm. On the fourth-harmonic optical signal, , this near-field signal strength is more than 20 times above the noise level. Such a near-field enhancement is similar to what has been observed in earlier work and what is expected from the interaction of a gold tip and a gold surface [23,29].
For comparison, the measurements of the optical signals and are repeated with the uncoated quartz substrate and are shown in Figs. 2(c) and 2(d), respectively. The DC signal for the uncoated quartz microscope slide is much stronger modulated than in the case of the gold-coated sample [Fig. 2(c)], showing that the interfering fields reflected from the tip shaft and from the quartz surface are well balanced. There is no near-field contribution to discernible in Fig. 2C. Even when demodulating the photodiode signal, the effect when approaching the uncoated sample to the gold tip is weak: does not display any deviation from the behavior far from contact [blue curve in Fig. 2(d)]. The signal shows a small roll-off near contact, of less than one third of its maximum amplitude, and simultaneously displays an increase of slightly less than its signal amplitude out of contact [green and red curves in Fig. 2(d)]. Thus, there is evidence of a near-field signal when demodulating at the third or fourth harmonic, but it seems still overrun by background signal or is on the order of the background signal .
Finally, we turn to the optical signals measured when approaching the in-line interferometer, i. e., a quartz substrate coated with a ~20-nm thick gold film and a ~200-nm thick SiO2 film on top of the gold film, to the gold nanotip. The modulation depth of the DC signal is in between that of the gold-coated and the uncoated sample [Fig. 2(e)], indicating a lower reflectivity of the in-line interferometer gold film than that of the gold-coated substrate. However, the modulation is clearly sufficiently strong to facilitate using as a reference field in our in-line interferometer homodyne scheme. This can be seen more clearly in the approach curves shown in Fig. 2(f): There is a near-field contribution discernible in all three signals , , and . The near-field increase is less pronounced than in the case that the tip is directly in contact with the gold film; the fourth-harmonic signal shows an increase of 7 times the noise level (compared to 20 times observed for the gold film). Considering that the near field signal that is measured when the gold tip is in contact with a glass surface [Fig. 2(d)] is just on the order of the noise level, we conclude that the enhancement by a factor 7 is due to interference of the near field and the field reflected from the semi-transparent gold film, .
Thus, on the one hand the multi-layer structure of the in-line interferometer indeed seems to enable the measurement of rather small near-field contributions, which can hardly be detected otherwise. On the other hand, the measured signals are a result of mixing on the field level, and knowledge of the electric field strengths of and is required in order to determine the actual near-field strength. In the next section we derive expressions that allow disentangling the contributions of the fields to each of the measured signals to .
4. Analysis of the interfering fields
In all cases investigated experimentally in Sec. 3, we consider the measured signal as the result of interference of the three electric fields , , and , as already briefly mentioned above. This section aims at disentangling the experimentally measured signals in order to discriminate the near field signal from the background contribution. For this, we first derive an analytic expression for the measured signals up to the fourth order of the tip modulation frequency, based on approximating the individual electric field strengths and by Fourier sums.
After the expressions are derived in Sec. 4.1, in the following Sec. 4.2 we compare them to the measured signals. Together, they will allow us to estimate the experimental conditions necessary for an “artefact-free” measurement of the near-field signal, i.e., the optimum sample properties and the demodulation order that enable to obtain a pure near-field signal with negligible influence of the background field.
4.1 Analytical expressions for the measured signals
The signals are measured with integration times much longer than the inverse of the light carrier frequency and even of the pulse repetition frequency; hence we can restrict the following considerations to temporal variations on the order of the tip modulation period. The measurement takes place at the detector, which is placed at a distance of several tens of cm from the light-sample-interaction region. At this position, we can describe the light as plane waves and neglect any lateral variation of the electric field strength. The considered electric fields are quasi-monochromatic and quasi-static plane waves, the only dependencies considered in this section are the tip-sample distance z, and the three different samples we investigated. This translates into changes of the field amplitudes or the relative phases of the three interfering fields, which manifest as variations of the measured signal.
The sample and the origin of the interfering fields are depicted in Fig. 3. The reference field is the part of the incident light that is reflected before reaching the nanotip and the tip-sample-interaction region and does not depend on the tip-sample distance. Furthermore, we chose to carry the reference phase, , such that becomes a constant in our frame of reference:
The background signal is scattered back from the gold nanotip. Hence it acquires a phase shift with respect to the reference field, according to the pathway difference of the two. The pathway of is longer by twice the tip-sample distance plus a constant distance d, which combines the distance from the apex, at which the backscattering from the shaft occurs, and the thickness of the glass layer in the case of the in-line interferometer. The pathway multiplied with the wave vector determines the phase of , together with a phase shift that can occur due to the reflection:
Depending on the reflectivity of the sample, i. e., of the semitransparent gold layer, multiple reflections between this layer and the tip can alter the distance dependence of the background field. For the samples investigated here, we found that one additional reflection is sufficient to describe the measured curves:Equation (3) is used later to disentangle background and near-field contributions to the measured signals. Furthermore, for the monochromatic measurements that are analyzed first, it is sufficient to treat the phase shift due to the fixed distance d as a constant and to combine it with the phase . This distance becomes important, however, for the spectral measurements presented in Sec. 5. For broad spectra the wavelength dependence of k results in a spectral phase and hence the interference of the three fields must show spectral modulation. In the following derivation of an expression for the measured signals, for the sake of simplicity, we use the Eq. (2) to describe the background field and will expand the derived expressions to include an additional reflection later.
Finally, as the near field we denote light that is scattered from the tip-sample-interaction region into the far field, after at least one interaction with the tip dipole and a dipole in the sample (see inset on the right of Fig. 3). The process can be described in the framework of dipole-dipole-coupling between sample and tip as introduced by B. Knoll and F. Keilmann  and propagation of the point-dipole-like excitation via the dyadic Green’s function . The incident electric field excites the z-oriented tip dipole and creates a polarization with the tip polarizability tensor . The polarization is the source of a point-dipole-like excitation at the tip position and emits a secondary field, which in turn induces an image dipole in the sample, if the tip-sample-distance is roughly equal to or smaller than the apex radius of curvature. This image dipole, whose dipole moment is determined by the complex dielectric function of the sample material, emits an electric field , which enhances the incident field at the tip position, such that the tip dipole moment becomes:
The so enhanced tip dipole leads to the radiation of an electric field , which is described by the dyadic Green’s function :
In the case of strong coupling of the incident field and the excited dipoles, potentially more than two consecutive scattering events have to be considered in a similar fashion as described above. Here, a self-consistent model can be applied to yield an effective polarizability . In our experimental scheme, however, the tip dipole moment is dominant over the image dipole in the sample, and the main contribution to fields radiated out of the tip-sample interaction region stems from the tip dipole enhanced by the image dipole. We treat the conical tip as a small metal sphere with radius R and with the polarizability , where is the complex dielectric constant of the tip material . In this case, Eq. (5) is sufficient to describe the radiated field. This radiated field consists of two terms; the first, results in a constant field contribution due to the tip dipole alone. As the tip-sample distance is changed, the amplitude of this first term does not change, but the phase changes with respect to the background field in the same fashion as was found before for the background field . Hence this first term can simply be considered a contribution to the background field. The second term , in contrast, depends strongly on the tip-sample distance and approaches zero for large z. If Eq. (5) was evaluated for the position given by the cross section of beam path and detector plane, and the constant first term was subtracted, the resulting field would yield the near-field contribution to the measured signal, i. e.,
Due to the strong distance-dependence of the dipole-dipole coupling, the near field intensity measured in the detector plane decreases exponentially with increasing tip-sample distance, and a phase shift due to the dipole-dipole coupling is taken into account:Figs. 2(b), 2(d), and 2(f) yield a near-field decay length of 8 nm.
The latter two fields, and are varying as a function of the tip-sample distance , which itself is a periodic function with period T: , where is the inverse of the tip modulation frequency. The distance can be written as a sinusoidal function with the modulation amplitude M, centered at the average tip-sample distance :23]:
Figure 4 shows the absolute of the Fourier coefficients for our experimental parameters, specifically for a wavelength and the tuning fork modulation amplitude , as a function of demodulation order n in a bar diagram. The red bars are the background-field coefficients normalized to the zeroth order coefficient, i. e., , and the blue bars the according near-field coefficients . It is noteworthy that not only do both coefficients decrease with demodulation order, but that the relative strength of the background decreases much more rapidly than that of the near field. This is in agreement with the measurements presented in Fig. 2, where the near-field contribution becomes more clearly visible as the demodulation order increases, as well as with observations in earlier works. The increase of the near-field-to-background-ratio with demodulation order forms the basis for higher-order demodulation SNOM [23,29].
Any signal that is measured in the detector plane is proportional to the absolute square of the total field . Inserting Eqs. (1), (11) and (12) and executing the absolute square gives
The power impinging on the photodiode is
Here, the index nf denotes the demodulation frequency, is the gain parameter of the lock-in detector, and is the phase between modulation waveform and detected signal. When measuring with the lock-in detector, the influence of this phase is eliminated by actually recording the amplitude, i. e., the geometrical average of measured for one phase setting and measured for a second phase setting . In our calculations the same effect is achieved easily by evaluating the integral of Eq. (19) for . The integral, performed over time intervals , is zero unless the demodulation frequency matches the angular frequency of the Fourier component under consideration.
The respective combinations of , , and that contribute to the measured signals can easily be extracted from the expression for given in Eq. (16). Because the highest order demodulation that can be measured with our 210-kHz line camera is the fourth order, we consider only Fourier coefficients up to this order, i. e., we restrict the sums in Eq. (17) to . The unmodulated signal then becomes:Eq. (20) can be simplified:Eq. (21) replicates the measured curves in Figs. 2(a), 2(c), and 2(e) quite well: they describe the interference of two fields with a phase varying as the distance between tip and sample increases, and with a contrast given by the respective field strengths of background and reference field.
Similarly, the signals measured at the first and higher harmonic demodulation frequencies, to , can be extracted from Eq. (16). After applying the same approximations as enumerated above for the example of , the less dominant terms are neglected, and we obtain the following four approximated expressions for to :
The relevant Eqs. (21)-(25) describe signal detection after the interference of vectorial fields. They are simplified to terms of products of two fields each, with only the three field amplitudes and phases and the near-field decay length as input parameters. Typically, not all three vector components contribute with comparable strengths, such that a full vectorial treatment is not required. In our experiment, the incident light is linearly polarized in the plane parallel to the table, corresponding to the y-direction given in Fig. 1. The reference field consists of light directly reflected from the semi-transparent gold film or from the uncoated surface of the substrate, which in both cases results in a purely y-polarized reference field. The background field , which is reflected off the cone-shaped surface of the gold tip, is expected to be mainly polarized along the y-direction, but to carry also a weak x-component. The near field is constituted of light that is scattered out of the near-field interaction region of sample and tip into the detected far field, as described above [Eqs. (4) and (5)]. The emission pattern of the coupled system of tip dipole and its image dipole in the sample is transformed by the high-NA objective into a radiation pattern that propagates back along the illumination path. Earlier measurements have shown that this light is radially polarized with a high degree of polarization . In the in-line homodyne detection scheme that is employed here, however, the near field contribution is only detected by mixing with the y-polarized reference field or with the mainly y-polarized background field. This restricts the near-field detection to approximately half the signal, namely the near field’s y-component. For this reason, a scalar description of the interference is sufficient. This is achieved by substituting with , with , and by substituting with in Eqs. (21)-(25).
4.2 Near-field contribution in the measurements
The reference field strength is measured directly as the unmodulated signal with the tip removed from the setup, setting in Eq. (21). For the gold-coated quartz sample, the power measured with the SiPD is , which, assuming a beam cross section of , corresponds to the reference field strength . The background field strength can be estimated rather precisely from the modulation depth on the signal in Fig. 2(a), which originates from the cosine-term in Eq. (21), with the result and the ratio . It should be noted that it is not possible to directly obtain a value for from the unmodulated signal since it is by far dominated by the background and reference fields. No near-field contribution is discernible in the measurement shown in Fig. 2(a). This is the case for all three substrates.
The derived expressions 22-25 for the optical signals to are compared to the measured approach curves, using the values and obtained from the measured signal in Fig. 2(a), and using the phase for the near field, , and the phase for the background field, , to manually adapt the shape of the calculated curves to the measured signal. Furthermore, for the gold-coated quartz substrate the effect of multiple reflections can be seen clearly from the deviation of especially from a single-sinusoidal behavior [Fig. 2(b)]. This is taken into account by using Eq. (3) to describe the background field, adding the reflection coefficient r and the second phase as adaptation parameters. For the gold-coated quartz substrate, the reflection coefficient is between and 0.45.
As an example, Fig. 5(a) shows the calculated curves and (dashed red curves) together with the experimentally measured approach curves (: blue curve, : green curve). With the above mentioned adjustable parameters, the derived expressions reproduce the measured curves quite closely. As a result of comparing the measurement to the derived expressions, we obtain on the one hand for , which represents a direct measure for the near-field contributions to the measured signals, and on the other hand the contributions that arise due to the background light scattered from the tip shaft, i. e., , , and . In Fig. 5(b), these values are plotted as bar diagrams as a function of demodulation order, normalized to . Both signal contributions decrease exponentially with increasing demodulation order, and as expected for a gold surface, the background signal decreases much faster than the near-field signal, such that for the near-field contribution already surmounts the background, and that for the background contribution amounts to only ~2.5%.
With a similar measurement of the pure reference power, we find for the uncoated quartz substrate the much smaller reference field strength and the background field strength , i. e., . The absence of a semitransparent gold film results in more light reaching the tip and hence increased scattering from the tip shaft, while the reference field is created only by a relatively weak reflection from the glass surface. As before, there is no near-field contribution discernible. Again, the derived expressions Eq. (22)-(25) are adapted to the measurements by manually varying the phases of background and near-field light, , , and . The reflectivity of the uncoated quartz is reduced to about half that of the gold-coated quartz samples, but due to the high background-to-reference ratio multiple reflections between tip and sample again have a high influence on the over-all signal [Fig. 5(c)]. Compared to the gold-coated quartz substrate, the high background-to-reference ratio of the uncoated quartz substrate results in a much stronger influence of the background-related signal components even at high demodulation orders: up to the fourth order near-field- and background-related signal components are of comparable strength [see Fig. 5(d)]. From this measurement it is clear that the reference signal needs to be increased in order to measure predominantly the near-field signal at demodulation frequencies that are experimentally easily accessible.
As the last substrate, we evaluate the approach curves for the in-line homodyne interferometer, i. e., for the gold- and glass-coated quartz substrate. Here the reference is again increased due to the semitransparent gold film, with and , i. e., . The derived expressions Eqs. (22)-(25) are adapted to the measurements like described before, and as examples, and are plotted in Fig. 5(e). In this case, there is still a small deviation between the measured and the calculated curves for apparent, and the curvature of at small tip-sample distances of could also not be entirely reproduced. This observation points towards somewhat more complicated multiple reflections than accounted for by our simple model, e. g., reflections not only between the tip and gold film but also between tip and substrate surface. The near-field and background contributions to the measured optical signals are plotted as a function of the demodulation order in the bar diagram in Fig. 5(f), where one can see that both signal contributions decrease exponentially with increasing demodulation order. Similar to the gold-coated substrate, also for our in-line interferometer, the background signal decreases faster than the near-field signal. For the near-field contribution surmounts the background, and at the background contribution amounts to only ~7%.
In conclusion, for the uncoated quartz substrate the reference and the background field are of comparable strength. Hence, for this case, cross terms not only between any higher order near-field terms and the reference field contribute to the measured signals, but also between higher order near-field terms and the background term have considerable influence. For uncoated glass substrates, a measurement exploiting near-field contrast will be possible only for higher demodulation orders than accessible to us in this work. For both metal-coated quartz substrates, in contrast, , such that the cross terms between higher-order coefficients and, and the reference field dominate. The faster decay of with increasing demodulation order then nearly completely removes the dependence on the unknown background field. The dominance of the near-field signal is a result of mixing the near field with a strong reference field, i. e. of the in-line homodyne interferometer formed by the buried gold film.
5. Broadband near-field spectroscopy
For broadband near-field spectroscopy we use a titanium:sapphire laser with a spectral bandwidth exceeding 100 nm as a broad-bandwidth excitation laser source [see laser input spectrum in Fig. 6(a)]. The APD and lock-in detector are replaced with a monochromator equipped with a fast line camera. Complete spectra are recorded at a rate of 210 kHz at fixed tip-sample distances. Figure 6(b) shows the tuning-fork amplitude that is used as the control parameter, as a function of tip-sample distance. Colored circles mark the positions at which spectra are recorded. For a first demonstration of spectrally resolved near-field measurements, we insert our in-line homodyne interferometer as the sample, i. e., a quartz substrate coated with a ~20-nm thick gold film and a ~200-nm thick SiO2 film on top of the gold film. As we have shown in Sec. 4.2, the reflection off the semitransparent gold film creates a reference field strong enough to amplify the near-field contributions above the background-related signal contributions. The near field, however, is created at the quartz surface, which in itself gives a weaker signal compared to a gold surface and is thus a more realistic test case for near-field spectroscopy of future samples. Furthermore, the spectral response of both a gold film and a quartz substrate is rather flat in the spectral range investigated here. The recorded spectra are post-processed to extract spectra demodulated at the n-th order of the modulation frequency : the signal recorded by each pixel as a function of time is multiplied by a factor and integrated over time [emulating the effect of the lock-in detector, see Eq. (19)].
This results in demodulated spectra , which are shown exemplary for the first- and the fourth-order demodulation in Figs. 6(c) and 6(d), respectively. The green-to-blue curves are measured in close proximity to the surface, with the darkest blue being the closest, and the red curve represents a spectrum that is recorded at a larger tip-sample distance, where the near-field contribution is vanishingly small.
The measured first-order demodulated spectra displayed in Fig. 6(c) have a spectral shape that generally differs from the input laser spectrum. Furthermore, this spectral shape varies with tip-sample distance, which is most apparent in the spectrum recorded at a large distance (red curve), but can also be seen in the other curves, where the tip-sample distance is varied only on a small scale of .
In order to explain the measured spectra we have expanded the theory developed for quasi-monochromatic fields in Sec. 4.1 to include the wavelength dependence of the interfering electric fields. Since the dielectric functions of both gold and quartz are nearly constant in the investigated wavelength region between 700 and 860 nm, we have assumed a flat spectral response of the sample. The tip polarizability of the tip can be estimated assuming a spherical dipole as described above, which results in a non-resonant characteristic of the tip in this spectral region, with changes of ~6% of the real part and negligible imaginary part of the polarizability. In good approximation, , and have the spectral shape of the square root of the laser intensity spectrum and a flat spectral phase.
The phase shift between reference and background field, now depends on the tip-sample distance and on the wavelength, leading to spectral interference in signals with sufficiently strong background contribution. The same is true for the background field that is reflected between the gold film and the tip a second time and carries the phase . The Fourier coefficients of the background field are also a function of the wavelength, but this has a much weaker influence on the observed spectra. With this simple expansion of the theory, the general behavior observed in the measured spectra is nicely reproduced: the calculated spectra shown in Fig. 6(d) show strong spectral modulation that varies considerably when the tip-sample distance is changed. We have observed that the shape of the spectra depends sensitively on the phase offset, and , such that some spectral components can vanish completely from the calculated spectra by adjusting these phases. Thus, spectral interference is the dominant effect that shapes the spectra. This makes it difficult to extract quantitative information on the sample response when ignoring those interferences.
This observation is emphasized, when comparing the measured and calculated spectra shown in Figs. 6(e) and 6(f), respectively. The second-order demodulated measured spectra also differ from the laser input spectrum, but they are also markedly different from the spectra in Figs. 6(c) and 6(d). Also within the spectra , each individual spectrum differs from those recorded at other tip-sample distance, which is most clearly visible for the spectrum recorded at the largest tip-sample distance (red curve). Knowing that the signal is composed of different terms of interfering fields than [compare Eqs. (22) and (23)], it is clear that spectral interference between the fields should lead to quite different measured and calculated spectra. From this, it is clear that such interference can easily obscure true near-field spectral information.
In contrast, the fourth-order demodulated spectra shown in Fig. 6(g) closely resemble the laser input spectrum, as expected for the sample with a flat spectral response, and they retain their over-all shape when the tip-sample distance is changed. As observed in the quasi-monochromatic measurements, the background-related signal contribution and hence also spectral interference are mostly suppressed when demodulating at the fourth order. The amplitude of the spectra decreases strongly with increasing tip-sample distance, indicating that these spectra are mainly governed by the near field. This is verified by the calculated spectra shown in Fig. 6(h), which are governed by the cross term of near field and reference field, and which are in very good agreement with the measured spectra.
Note that, in near-field spectroscopy with this in-line homodyne interferometer, the amplitude and phase of the near field are easily obtained: Dividing the envelope of by the square root of the separately measured reference spectrum would yield the near field amplitude, and the phase difference would show as spectral modulation, as known from spectral interferometry . The amplitude and phase of the near field will be determined by the complex dielectric function of the sample material via the effective polarizability of the probe (see Eqs. (5) and (6), and ).
6. Summary, discussion and outlook
In this work, we have analyzed the signal in scattering-type scanning near-field optical microscopy on the field level, and we have identified and designed a layered structure that allows disentangling near-field and background-related signal contributions by mixing the near field with a strong reference field. The layered structure was realized by depositing a thin gold film on the sample substrate and covering it with a thin dielectric layer and forms an inherently phase-stable in-line interferometer for. We have shown that this efficiently amplifies the near field and suppresses the background light, such that when demodulating the signal with the third or fourth harmonic of the tip modulation frequency mainly the near field is detected.
Both the interferometer and the gold nanotaper used as a near-field probe support broad-bandwidth spectroscopy over the visible and near-infrared wavelength range. Complete spectra were recorded in tip-modulated s-SNOM using a fast line camera that enables post-measurement extraction of spectra demodulated with up to the fourth-order harmonic frequency. With the developed multi-layer structure and with the fast line camera, we have measured pure near-field spectra over a broad bandwidth in the visible spectral region.
Our measured and calculated optical signals verify and demonstrate the challenging effect of background signals in scattering-type SNOM. Interference between light that is reflected from the sample and light that is scattered from the tip shaft dominates the measured signal, in the case of an uncoated sample even if the signal is demodulated at the fourth harmonic of the tip modulation frequency. For broad-bandwidth spectroscopy, this results in spectral interference that basically determines the shape of the measured spectra. In this work, we have shown that a reference field of sufficient amplitude, namely of roughly 50-fold amplitude of the background field, can achieve efficient background suppression. The reference field then amplifies the near field such that at demodulation at the third or fourth harmonic of the tip modulation frequency results in the very precise detection of the near field. Specifically, we have created the reference field within the substrate of the sample, thereby realizing an inherently stable in-line interferometer.
In this work, a reference field with suitable amplitude is provided by 30-50% reflection of the incident laser field off a ~20-nm thick gold film. This semitransparent gold film transmits sufficient light to create a near field, while at the same time supplying a reference field for amplification of the near field above the background contributions. Note that the optimum reflectivity of the gold layer of a few tens of percent is dictated not by the sample to be investigated but by the amount of background field that needs to be suppressed. A gold-dielectric interface however, supports surface plasmons, which could interact with the tip and with a sample applied to the gold surface. This could affect near-field spectra measured of the sample. To avoid such disturbance, we have covered the gold film with a quartz layer of a 200-nm thickness. This is longer than the plasmon decay length, but also sufficiently thin to not result in spectral modulation of the measured spectra. Alternatively, one may use a substrate made of a transparent dielectric material with high refractive index. A somewhat lower reflectivity between 10 and 20% could be realized in a trade-off between ease of substrate production and near-field amplification.
While we have concentrated on overriding the background-related signal contributions with an amplified near-field related signal, it would be even more advantageous to reduce the detrimental effect of the background field. Reduction of light scattered from the tip shaft would greatly improve the potential of s-SNOM. Such a reduction of background light would require changing the dielectric function of the tip material, i. e., making the tip in essence transparent to the incident laser light. Creating a near-field signal, however, requires a strong tip dipole. Both requirements could be combined, for example, by placing a metal sphere on a transparent mount such as a dielectric taper . A metal sphere offers a large dipole moment, but has a narrow resonance. Thus, while such a tip on the one hand could hold great potential to improve the signal-to-background ratio in s-SNOM, it would, on the other hand, considerably reduce the bandwidth for spectroscopy. There is a trade-off between background reduction, tip dipole moment, and spectral bandwidth. In our experience, the gold nanotapers that were used in this work optimize dipole moment and spectral bandwidth, but introduce a relatively large background signal that requires additional measures for background suppression.
In summary, we have made considerable progress towards broadband s-SNOM spectroscopy in the visible spectral range. We have realized an inherently phase-stable in-line interferometer for mixing the near field with a strong reference field by depositing a thin gold film on the sample substrate and covering it with a thin dielectric layer. We have shown that this efficiently amplifies the near field and suppresses the background light. Using a fast line camera we have recorded complete spectra in tip-modulated s-SNOM. By post-measurement extraction of spectra demodulated with the fourth-order harmonic frequency we have acquired pure near-field spectra in over a broad bandwidth of the visible spectral region.
Our results open up a new approach towards quantitative, ultrahigh resolution, broadband near-field scattering spectroscopy. Currently we are applying this new interferometric broadband near-field spectroscopy to observing the coupling in organic-metallic hybrid nanostructures.
Deutsche Forschungsgemeinschaft (SPP1391, GRK1885); Niedersächsisches Ministerium für Wissenschaft und Kultur (LGRK “Nano-Energieforschung”); The Korea Foundation for International Cooperation of Science and Technology (K20815000003); The German-Israeli Foundation (1256).
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